Harmonic analysis deals with the mathematical representation of combinations of waves. In the abstract worlds of mathematics, trigonometric functions (like a sine wave) are often used to represent waveforms, but these usually present simple waves. In the real world, waves tend to be more complex. By combining the simple waveforms in many different ways, these complex forms can be constructed and studied.

Primitive harmonic series were used by the Babylonians to construct tables of the positions of astronomical bodies.

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“I confess that, in 1901, I said to my brother Orville that men would not fly for 50 years. Two years later, we ourselves were making flights. This demonstration of my inability as a prophet gave me such a shock that I have ever since distrusted myself and have refrained from all prediction.”